1. Field of the Invention
The present invention relates to a digital filter system, more particularly, to a digital filter system which can change the position of the pass band and/or the width of the pass band.
2. Description of the Related Art
Band Pass type digital filters are adapted to various technical fields, and recently, digital filter systems which can vary the position (the central frequency, and the upper and lower limit frequency) and/or the width of the pass band have been proposed.
For example, the U.S. Pat. Nos. 5,479,362 and 5,530,660, which is the divisional application of the former patent, disclose a variable central frequency type band pass filter system shown in FIG. 6. As shown, the variable central frequency type band pass digital filter system comprises:
an N order band pass digital filter 121 for filtering an input digital signal in accordance with filter coefficients {a.sub.k1, a.sub.k2 and b.sub.k1 } (k=1, 2, . . . , N/2; N is an even number), and for outputting the filtered signal; PA1 a first memory 113 for storing filter coefficients {a.sub.k1 (f.sub.a), a.sub.k2 (f.sub.a) and b.sub.k1 (f.sub.a)} and {a.sub.k1 (f.sub.b), a.sub.k2 (f.sub.b) and b.sub.k1 (f.sub.b)} of known band pass digital filters having a constant band pass width whose center frequencies are f.sub.a and f.sub.b, and filter coefficients {a.sub.k1 (f.sub.r), a.sub.k2 (f.sub.r) and b.sub.k1 (f.sub.r)} of the known band pass digital filter having a constant pass band width whose center frequency is f.sub.r ; PA1 a second memory 115 for storing linear coefficients K.sub.akj and K.sub.bk1, which are calculated in accordance with equations (1) and (2) by using the filter coefficients stored in the first memory 113; EQU K.sub.akj =a.sub.kj (f.sub.b)-a.sub.kj (f.sub.a)!/(f.sub.b -f.sub.a) EQU k=1,2, . . . , N/2 j=1,2 (1) EQU K.sub.bk1 =b.sub.k1 (f.sub.b)-b.sub.k1 (f.sub.a)!/(f.sub.b -f.sub.a) EQU k=1,2, . . . N/2 (2) PA1 displacement setting means SV for setting displacement m.DELTA.f between target center frequency and the predetermined center frequency f.sub.r of said band pass digital filter 121; PA1 multiplication means 117 for obtaining m.DELTA.f.multidot.K.sub.akj and m.DELTA.f.multidot.K.sub.bk1 by multiplying the displacement m.DELTA.f, supplied from said displacement setting means SV, by the linear coefficients K.sub.akj and K.sub.bk1 stored in said second memory 115; PA1 adding means 119 for obtaining a.sub.k1 (f.sub.r)+m.DELTA.f.multidot.K.sub.ak1, a.sub.k2 (f.sub.r)+m.DELTA.f.multidot.K.sub.ak2, and b.sub.k1 (f.sub.r)+m.DELTA.f.multidot.K.sub.bk1 by adding the products obtained by said multiplication means 117, to a corresponding one of the filter coefficients stored in said first memory 113; and PA1 setting means 111 for setting the central frequency of said band pass digital filter 121 to f.sub.r +m.DELTA.f by setting the values a.sub.k1 (f.sub.r)+m.DELTA.f.multidot.K.sub.ak1, a.sub.k2 (f.sub.r)+m.DELTA.f.multidot.K.sub.ak2, and b.sub.k1 (f.sub.r)+m.DELTA.f.multidot.K.sub.bk1, obtained by said adding means 119, as the filter coefficients {a.sub.k1, a.sub.k2 and b.sub.k1 } of said band pass digital filter 121. PA1 an N order band pass digital filter 121 for filtering an input digital signal in accordance with filter coefficients {a.sub.k1, a.sub.k2 and b.sub.k1 } (k=1, 2, . . . , N/2; N is an even number), and for outputting the filtered signal; PA1 a first memory 113 for storing filter coefficients {a.sub.k1 (B.sub.a), a.sub.k2 (B.sub.a) and b.sub.k1 (B.sub.a)} and {a.sub.k1 (B.sub.b), a.sub.k2 (B.sub.b) and b.sub.k1 (B.sub.b)} of the known band pass digital filter having a constant center frequency whose pass band widths are B.sub.a and B.sub.b, and filter coefficients {a.sub.k1 (B.sub.r), a.sub.k2 (B.sub.r) and b.sub.k1 (B.sub.r)} of the known band pass digital filter having the constant center frequency whose pass band width is B.sub.r ; PA1 a second memory 115 for storing linear coefficients K.sub.akj and K.sub.bk1, which are calculated in accordance with equations (3) and (4) by using the filter coefficients stored in the first memory 113; EQU K.sub.akj =a.sub.kj (B.sub.b)-a.sub.kj (B.sub.a)!/(B.sub.b -B.sub.a) EQU k=1, 2, . . . N/2 j=1, 2 (3) EQU K.sub.bk1 =b.sub.k1 (B.sub.b)-b.sub.k1 (B.sub.a)!/(B.sub.b -B.sub.a) EQU k=1, 2, . . . N/2 (4) PA1 displacement setting means SV for setting displacement m.DELTA.B between target pass band width and predetermined pass band width B.sub.r of said band pass digital filter 121; PA1 multiplication means 117 for obtaining m.DELTA.B.multidot.K.sub.akj and m.DELTA.B.multidot.K.sub.bk1 by multiplying the displacement m.DELTA.B, supplied from said displacement setting means SV, by the linear coefficients K.sub.akj and K.sub.bk1 stored in said second memory 115; PA1 adding means 119 for obtaining a.sub.k1 (B.sub.r)+m.DELTA.B.multidot.K.sub.ak1, a.sub.k2 (B.sub.r)+m.DELTA.B.multidot.K.sub.ak2, and b.sub.k1 (B.sub.r)+m.DELTA.B.multidot.K.sub.bk1 by adding the products obtained by said multiplication means 117 to a corresponding one of the filter coefficients stored in said first memory 113; and PA1 setting means 111 for setting the pass band width of said band pass digital filter 121 to B.sub.r +m.DELTA.B by setting the values a.sub.k1 (B.sub.r)+m.DELTA.B.multidot.K.sub.ak1, a.sub.k2 (B.sub.r)+m.DELTA.B.multidot.K.sub.k2, and b.sub.k1 (B.sub.r)+m.DELTA.B.multidot.K.sub.bk1, obtained by said adding means 119, as the filter coefficients {a.sub.k1, a.sub.k2 and b.sub.k1 } of said band pass digital filter 121. PA1 a digital filter for filtering an input digital signal in accordance with filter coefficients {a.sub.k1, a.sub.k2, b.sub.00, b.sub.k1, b.sub.k2, c and d} (k=1, 2, . . . ,N/2; N is an even number), and for outputting the filtered signal; PA1 calculation means for calculating each of the filter coefficients {a.sub.k1, a.sub.k2, b.sub.00, b.sub.k1, b.sub.k2, c and d} in accordance with equations (5) to (11) by using pass band position data x and pass band width data y; and PA1 setting means for setting the filter coefficients calculated by said calculation means to said digital filter. ##EQU1## PA1 a digital filter for filtering an input digital signal in accordance with filter coefficients FC.sub.h (h=1, 2, . . . , n; n is a natural number), and for outputting the filtered signal; PA1 calculation means for calculating the filter coefficients FC.sub.h in accordance with equation (13) by using pass band position data x and pass band width data y; and PA1 setting means for setting the filter coefficients FC.sub.h calculated by said calculation means to said digital filter. ##EQU3## PA1 a digital filter for filtering an input digital signal in accordance with filter coefficients, and for outputting the filtered signal; PA1 parameter storage means for storing parameters for calculating said filter coefficients defined by a non-linear polynomial for the position and/or the width of the pass band of said digital filter; PA1 filter coefficient calculation means for calculating said filter coefficients, based on said parameters stored in said parameter storage means, and a target position and/or a target width for the pass band of said digital filter; and PA1 setting means for setting the filter coefficients calculated by said filter coefficient calculation means to said digital filter.
The Patent also discloses a variable band width type band pass digital filter system.
This variable band width type band pass digital filter system, as shown in FIG. 6, comprises:
According to the technique disclosed in the above described patent, the position or the width of the pass band of the digital filter can be varied with a relatively smaller memory capacity and less calculation.
According to the digital filter system disclosed in the above described patent, the filter coefficients are obtained by linear approximation.
When the position or the width of the pass band changes relatively large, however, the filter coefficients change non-linearly. Therefore, an error between the calculated filter coefficients and the ideal filter coefficients occurs. Because of the error, the filter characteristics are degraded.
For example, FIG. 5 exemplifies the changes in the filter coefficients when the pass band width is changed. It is apparent from FIG. 5 that the filter coefficients change non-linearly when the pass band width is changed greatly, and the error occurs when the filter coefficients are set by linear approximation.
Further, it is desired that the amount of data and the amount of calculation, necessary for obtaining the filter coefficients, are decreased.
Also desired are a high pass digital filter system which can exactly change lower limit frequencies of the pass band with less calculation, as well as the variable band width type band pass digital filter system, and a low pass digital filter system which can change upper limit frequencies of the pass band.